03833nam 2200613 450 991013479560332120200520144314.03-11-048030-13-11-048106-510.1515/9783110481068(CKB)3850000000001073(EBL)4718418(OCoLC)962793042(DE-B1597)466925(OCoLC)951141809(OCoLC)963114749(DE-B1597)9783110481068(Au-PeEL)EBL4718418(CaPaEBR)ebr11283245(CaONFJC)MIL964181(OCoLC)961059086(ScCtBLL)a80371dd-766f-4802-9ff9-c024f7263329(oapen)https://directory.doabooks.org/handle/20.500.12854/48863(CaSebORM)9783110480306(MiAaPQ)EBC4718418(EXLCZ)99385000000000107320161028h20162016 uy 0gerurcn#nnn|||||txtrdacontentcrdamediacrrdacarrierGraphs for pattern recognition infeasible systems of linear inequalities /Damir GainanovDe Gruyter2016Berlin, [Germany] ;Boston, [Massachusetts] :De Gruyter,2016.©20161 online resource (x, 147 pages)3-11-048013-1 Includes bibliographical references and index.Frontmatter -- Preface -- Contents -- 1. Pattern recognition, infeasible systems of linear inequalities, and graphs -- 2. Complexes, (hyper)graphs, and inequality systems -- 3. Polytopes, positive bases, and inequality systems -- 4. Monotone Boolean functions, complexes, graphs, and inequality systems -- 5. Inequality systems, committees, (hyper)graphs, and alternative covers -- Bibliography -- List of notation -- IndexThis monograph deals with mathematical constructions that are foundational in such an important area of data mining as pattern recognition. By using combinatorial and graph theoretic techniques, a closer look is taken at infeasible systems of linear inequalities, whose generalized solutions act as building blocks of geometric decision rules for pattern recognition.Infeasible systems of linear inequalities prove to be a key object in pattern recognition problems described in geometric terms thanks to the committee method. Such infeasible systems of inequalities represent an important special subclass of infeasible systems of constraints with a monotonicity property - systems whose multi-indices of feasible subsystems form abstract simplicial complexes (independence systems), which are fundamental objects of combinatorial topology.The methods of data mining and machine learning discussed in this monograph form the foundation of technologies like big data and deep learning, which play a growing role in many areas of human-technology interaction and help to find solutions, better solutions and excellent solutions. Contents:PrefacePattern recognition, infeasible systems of linear inequalities, and graphsInfeasible monotone systems of constraintsComplexes, (hyper)graphs, and inequality systemsPolytopes, positive bases, and inequality systemsMonotone Boolean functions, complexes, graphs, and inequality systemsInequality systems, committees, (hyper)graphs, and alternative coversBibliographyList of notationIndexInequalities (Mathematics)Graph theoryInequalities (Mathematics)Graph theory.516/.1Gainanov Damir(Damir N.),871838MiAaPQMiAaPQMiAaPQBOOK9910134795603321Graphs for pattern recognition1946278UNINA